Aufbau Principle

A common homework, quiz, or exam question in general chemistry courses might read, “What is the
ground state electron configuration for sodium?” If you are taking a chemistry class, you have probably
seen some variation of this question. Perhaps your instructor asked about a different element than
sodium, or perhaps you were asked to write an electron configuration for an ion instead of a neutral
atom. Regardless of the details involved, you can solve the problem by applying the Aufbau principle.

The term “Aufbau” comes from the German word for “building up,” and it describes how electrons fill
the energy levels in an atom (Atkins, 1986). To get a big-picture understanding of the Aufbau principle,
you can think about nature putting electrons into energy levels the same way a lazy librarian might fill a
shelf with books. Not wanting to do any heavy lifting, the lazy librarian would put books on the easy-to-
reach bottom shelf first. When that shelf filled up, the librarian would start filling the second shelf from
the bottom, and so on. Just as the lazy librarian wants to put books on the lowest shelf possible, nature
“wants” to put electrons in the lowest energy level possible.

Figure 1 shows how the lazy librarian would fill the (oddly shaped) bookshelf below with eleven books.
We could describe the configuration of the books by saying that there are two on the first shelf, two on
the second shelf, six on the third shelf, and one on the fourth shelf. If we know how many shelves we
have and how many books can go on each shelf, we can always predict how the bookshelf will fill. (For
the sake of the analogy, we are assuming that all books are the same size.)

Figure 1: The shelves fill in order from lower to higher

In order to describe how electrons are arranged in atom, we need some terminology, but we can
continue to visualize the bookshelf example in our minds. Each “shelf” with a specific height is
analogous to a subshell with a specific energy. You can think of the energy of the subshell as the height
of the shelf. Just as each shelf in figure 1 holds a specific number of books, each subshell will hold a
specific number of electrons. Electrons will fill the lowest energy subshell first, then the next lowest,
and so on.

The lowest energy subshell is the 1s orbital, which holds two electrons (just as our first shelf held two
books). The second lowest energy subshell is the 2s subshell, which holds two electrons, followed by
the 2p subshell. As you might guess from the bookshelf drawing, the 2p subshell holds six electrons.
Above the 2p subshell is the 3s subshell, capable of holding two electrons. The last subshell illustrated
in the bookshelf drawing is the 3p subshell, capable of holding six electrons.

Have you noticed a pattern? The s-subshells hold two electrons, while the p-subshells hold six electrons.
This is always true. Moreover, d-subshells and f-subshells (we’ll learn more about those in a moment)
hold 10 and 14 electrons, respectively. Be sure to memorize this information.

Now that we have established some terminology for discussing energy levels of electrons, we can
answer the question posed at the beginning of this discussion—“What is ground state electron
configuration for sodium?” First, we need to know how many electrons sodium has. According to the
periodic table, it has eleven. Next, we use the Aufbau principle to describe how the electrons build
up. Two can fill the 1s subshell, another two will fill the 2s subshell, six will fill the 2p subshell, and one
electron will occupy the 3s subshell. Hence, the electron configuration of sodium is 1s²2s²2p⁶3s¹.

In order to write electron configurations for any atom or ion in general, we need a way to memorize
the various subshells and the order in which they fill. While rote memorization works, learning this
information will be much easier if you mentally organize it. Figure 2 below illustrates a way to do this.

Figure 2, courtesy of Wikimedia Commons

Note that Figure 2 is fairly simple to memorize. The first column starts with the number 1, the second
column starts with the number 2, and so on. The subshells in the first column are all “s,” while the other
columns are “p,” “d” and “f” subshells, respectively. You can remember the order “s, p, d, f” by using a
silly-sentence mnemonic like “schnauzers prefer dog food”. Practice making Figure 2 without looking so
that you can reproduce it quickly in a test situation.

In addition to the numbers and letters, Figure 2 also has arrows. The arrows illustrate the Aufbau
principle. That is, they tell us the order in which the subshells fill. To see this, follow each diagonal line
in order. The first diagonal line tells us that the 1s subshell fills first. The second diagonal line shows
that the 2s fills next, while the third diagonal line says that the next subshells to fill are the 2p and 3s,
in that order. Once you have memorized Figure 2 and learned how to use it, you will be able to write
the electron configuration of an atom, provided that you know how many electrons go in each type of
subshell (s=2, p=6, d=10, f=14). A mnemonic to remember the sequence 2, 6, 10, 14 is to recall the first
5 odd numbers (1, 3, 5, and 7) and then multiply them by two. Writing electron configurations for ions
will follow the same process as writing electron configurations for atoms, but you will need to add or
subtract electrons as needed.

Let’s take a look at another example. Suppose the test questions says, “Write the ground state electron
configuration for S^2-.” Normally, sulfur would have 16 electrons (according to the periodic table).
However, S^2- must have two additional electrons in order to give it a charge of -2. That means we have
18 electrons to describe. Using Figure 2, we can put 2 electrons in the 1s subshell, 2 in the 2s, 6 in the
2p subshell, 2 in the 3s, and 6 in the 3p subshell. We would write our answer as: 1s²2s²2p⁶3s²3p⁶. Note
that the superscripts tell us how many electrons are in each subshell. If you add up the superscripts, you
get 18, the total number of electrons in S^2-. This is not a coincidence—always check the subscripts to
make sure they add up to the correct number of electrons.

As you have probably guessed, electron configurations for atoms with large atomic numbers soon
become unwieldy! For example, using Figure 2, we can see that the electron configuration for bromine
is 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁵. This configuration can be condensed by noting that 1s²2s²2p⁶3s²3p⁶
is the electron configuration for argon. Hence, the condensed electron configuration for bromine is
[Ar]4s²3d¹⁰4p⁵. The choice of argon was not arbitrary; it was based on the noble gas rule for writing
condensed electron configurations. In order to condense an electron configuration for an element,
locate that element on the periodic table and look for the noble gas one row above it. Look at the
electron configuration for your element and start adding up the superscripts in order until you reach the
atomic number of the noble gas, then replace that part of the electron configuration with the symbol for
the noble gas in brackets.

Before closing, I must offer a final caveat—not all atoms behave according to the rules described above.
Discussing all of the exceptions to the Aufbau principle is beyond the scope of this tutorial, but one
example of an exceptional element is copper, whose electron configuration is 1s²2s²2p⁶3s²3p⁶4s¹3d¹⁰
(Sterkewolf, n.d.). Transitions metals often fill their energy levels according to more complex set of rules
and do not appear to obey the Aufbau principle. Atoms that are in an excited state (as opposed to the
ground state), will have electrons in higher-than-expected energy levels. However, these examples are
not usually covered in basic undergraduate or high school courses.

Mastering the Aufbau principle may seem like a daunting challenge, but it will become simple with
practice. Below are two multiple choice questions to test your understanding of this important
chemistry concept.

References
Atkins, P. (1986). Physical chemistry. (3rd ed., p. 360). New York, NY: W.H. Freeeman and Company.
(2006, July 08). Klechkovski rule.svg [Print Photo]. Retrieved from http://en.wikipedia.org/wiki/File:Klechkovski_rule.svg

Sterkewolf, Z. (n.d.). Electron configuration of transition metals and ions: Mn vs. cu. Retrieved from http://chemwiki.ucdavis.edu/Inorganic_Chemistry/Electronic_Configurations/Electron_Configuration_of_Transition_Metals_and_Ions:_Mn_vs._Cu